Mystery solved by myself.
The cause of the problem: My version of IE v7.0.5730.13 somehow either "shrinks" the password field, or "inflates" the e-mail field. God knows why and how.
The old versions on my other PC (as well as Firefox) does not and therefore the two fields are of the same length and nicely vertically aligned.
The same problem appears in my "not-split" login page which you can see if you simply click http://haostaff.com/store/index.php?main_page=login . Some of you might see different lengths of the email and password fields, while some may see same length.
Knowing the cause, I have found the place to tweak it to try to make it look acceptable to all browsers. I increased the length of both fields so that they both (instead of one yes one no) break to the left to appear under the text titles.
The place that I did this is includes/templates/templates_default/templates/tpl_login_default.php
Cheers ... but the mystery about IE lingers.